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Math Help - Differentiating with respect to x^2 and 1/(1-x)... AP review problem

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    Differentiating with respect to x^2 and 1/(1-x)... AP review problem

    I'm reviewing my first semester of AP Calculus. While doing some review questions, I came across these two problems.


    1. If Differentiating with respect to x^2 and 1/(1-x)... AP review problem-codecogseqn-21.gif, find the derivative of Differentiating with respect to x^2 and 1/(1-x)... AP review problem-codecogseqn-22.gif with respect to Differentiating with respect to x^2 and 1/(1-x)... AP review problem-codecogseqn-23.gif.
    2. If Differentiating with respect to x^2 and 1/(1-x)... AP review problem-codecogseqn-24.gif, find the derivative of Differentiating with respect to x^2 and 1/(1-x)... AP review problem-codecogseqn-25.gif with respect to Differentiating with respect to x^2 and 1/(1-x)... AP review problem-codecogseqn-26.gif.



    I started manipulating the derivative notation in order to get the solution, but how do I continue this problem?
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    Re: Differentiating with respect to x^2 and 1/(1-x)... AP review problem

    (1) y = \sqrt{x^2+1}

    y^2 = x^2 + 1

    \frac{d}{dx^2}(y^2 = x^2 + 1)

    \frac{dy^2}{dx^2}= 1


    (2) let u = \frac{1}{1-x}

    \frac{du}{dx} = \frac{1}{(1-x)^2}

    y = x^2+x

    \frac{dy}{dx} = 2x+1


    \frac{dy}{du} = \frac{\frac{dy}{dx}}{\frac{du}{dx}} = (2x+1) \cdot (1-x)^2
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